To compare torsional responses from the two-phase model with that from the WLC model, we tested at a constant rate of supercoil accumulation, \(\Delta Lk=10\)  per second, comparable to the RNA polymerization rate during transcription elongation (i.e.,\(\sim \)  100 bp per sec), in which \(\Delta Lk=0.1\)  is injected into DNA for the RNA polymerase enzyme unwinding to synthesize one nucleotide[1]}, [2]}. The discontinuities on torque and extension curves are reproduced by the two-phase dynamic model, which reflect the buckling transition during plectoneme nucleation[3]}, [4]}, [5]}, [6]}, [7]}, [8]}. The torque and extension versus linking number curves suggest that the non-equilibrium effect of the supercoiling accumulation (from the growth of the plectonemic phase) induced by RNAP is constantly relaxed during each polymerization step or elongation cycle. Hence, such an RNA elongation process can be regarded as quasi-steady state. An obvious advantage of the currently developed two-phase dynamic model of DNA supercoiling comes from its trivial computational cost as we only deal with the slow degrees of freedom of the system. Besides, we performed simulations of the plectonemes growth under a constant torque since some studies also regarded RNAPs as a torsional motor which imposes a constant torque[9]}. We accordingly determined frictional coefficient due to slithering in plectoneme by calibrating with the WLC model.
